Carl Love

Carl Love

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9 years, 57 days
Natick, Massachusetts, United States
My name was formerly Carl Devore.

MaplePrimes Activity

These are answers submitted by Carl Love

I don't know whether you consider a typed command to be doing it "manually", or if that means via pen and paper to you. So, here's how to do it with a typed command: You say that you've "been given values of the quotient C__A0/C__AA". I will suppose that that given value is q. Then do

simplify(solve({-k*t = 1/C__A0 - 1/C__AA}, k), {C__A0/C__AA= q});
                        /      q - 1  \ 
                       { k = --------- }
                        \    C__AA t q/ 

I don't know how to do this (or much else) with menu-based commands. The presence of that side relation with q adds a level of complexity to menu-based iteractions.

You can create a custom type Monomial like this:

TypeTools:-RemoveType('Monomial'): #avoid silly warning
    'Monomial', #quotes protect against global reassignment of names
        local Var:= 'Y'[integer $ 2], Pow:= {Var, Var^rational};
        e::Pow or
            {Pow, Not({constant, 'satisfies'(e-> hastype(e, Var))})},
type(Y[1,-3]^(-7/4)*sqrt(t+x), Monomial);

type(Y[4,3]^3*sin(Y[1,2]), Monomial);

To understand the above, you should read the help pages for the types integer, fraction, and constant, the type operator satisfies, and the commands AddType and hastype. The type `*` and the type operators { },  specop, and Not are documented (minimally) on the page ?type,structure.

The above will not work in 2D Input or in some older versions of Maple. If you're using either of those, let me know.

When entering an integral as a Maple command (rather than simply for display), do not use "d". The variable of integration is determined by the variable immediately after the comma. The pretty-printed output will still show a "d" followed by a variable.

Use this:

Exponent:= (x::algebraic)-> 
    `if`(x=0, undefined, `if`(x=1, 0, `if`(x::{`^`, specfunc(`%^`)}, op(2,x), 1)))

So, the result is undefined if the term is 0, it's 0 if the term is 1, it's 1 if the term is not or 1 but has no explicit exponent, and it's the explicit exponent if one appears.

Note that non-numeric denominators always become multiplicands with their exponent negated in their internal representation.

There are two problems. The first is a syntax error in one of the boundary conditions. You've entered

varepsilon + delta*D@@2*(f)

You need to change that to

varepsilon + delta*(D@@2)(f)(LB)

The second problem is that you can't use infinity as the upper boundary UB; the current numeric BVP algorithms won't allow it. I changed UB to 5. I also changed Digits to 40 because a warning message advised raising it to 32. With these changes, I got through the first set of plots. Using different parameter values, it's very likely that you'll get to some boundary-layer effects, for which you'll get the error message "Newton iteration is not converging" or "initial Newton iteration is not converging". Fixing this problem (if it happens) is a much more subtle process. 

The Sieve of Eratosthenes is great for finding large sets of small primes, but it's useless (much too slow) for finding large primes. It seems like you're interested in finding large primes, such as those found by GIMPS. Below, I have implemented the Lucas-Lehmer test for Mersenne primes, which is the same algorithm used by GIMPS.

#Compute N mod (2^n-1) via bitwise operations. N must be < 4^n.
BitMod:= (N::posint, n::posint)->
    if ilog2(N+1) < n then N
    else `if`(ilog2(N) < n, 0, thisproc(add(Bits:-Split(N, n)), n)) 
#Check whether (2^p-1) is prime by Lucas-Lehmer algorithm.
IsMersennePrime:= proc(p::And(prime, Not(2)))
local s:= 4;
    to p-2 do s:= BitMod(s^2, p) - 2 od;
end proc:
IsMersennePrime(2):= true
#This Mersenne prime was discovered by computer in 1979:
memory used=2.65GiB, alloc change=0 bytes, 
cpu time=10.58s, real time=12.60s, gc time=6.48s

#Verify a negative case:

memory used=2.64GiB, alloc change=0 bytes,
cpu time=10.34s, real time=12.54s, gc time=6.39s

#Compare timings using default method not specific to Mersenne numbers:
memory used=3.73GiB, alloc change=61.50MiB, 
cpu time=59.81s, real time=63.96s, gc time=1.92s


memory used=2.78MiB, alloc change=0 bytes, 
cpu time=21.45s, real time=21.47s, gc time=0ns



To make your example work, all that you need to do is remove the export from in front of move in module dog. In other words, this works:

animal:= module()
option object;
    move::static:= proc(_self, $)
        print("In Animal class. moving ....")
    end proc
end module;
#create class/module which extends the above
dog:= module()
option object(animal);
    move::static:= proc(_self, $)
        print("In dog class. moving ....")
    end proc  
end module;

You can verify that the method overriding and polymorphism has been done properly.

To make that work in library code, the redefinition of move should be put in a ModuleLoad procedure, like this:

dog:= module()
option object(animal);
    ModuleLoad:= proc()
        move::static:= proc(_self, $)
            print("In dog class. moving ....")
        end proc;
    end proc
end module;

Like this:

PS:= PolyhedralSets:
    PS:-PolyhedralSet([[100,100]]), #point being tested

For real and b


returns what you want.

This can also be done with the two-argument form of arctan:

arctan(b, a)

Given any ordering method for the remaining numbers on the board, and always combining the two largest or smallest under that ordering, the following procedure will quickly do it:

Fold:= proc(F, Ord, S::list)
local H:= heap[new](Ord, S[]);
    while heap[size](H) > 1 do 
        heap[insert](F(heap[extract](H), heap[extract](H)), H)
end proc
F:= (x,y)-> 2*(x+y):
S:= [$1..2012]:

#Always pick the smallest 2 on the board:
CodeTools:-Usage(Fold(F, `>`, S));
memory used=9.95MiB, alloc change=0 bytes, 
cpu time=125.00ms, real time=125.00ms, gc time=0ns


#Always pick the largest 2 on the board:
CodeTools:-Usage(Fold(F, `<`, S));
memory used=14.05MiB, alloc change=0 bytes, 
cpu time=157.00ms, real time=154.00ms, gc time=0ns


#Choose two at random:
R:= rand(0..1):
CodeTools:-Usage(Fold(F, ()-> (R()=0), S));
memory used=12.05MiB, alloc change=0 bytes, 
cpu time=188.00ms, real time=176.00ms, gc time=0ns



If e is your expression, do 

eval(e, Units:-Unit= 1)

for tmp in op(THE_SUMS) do
for tmp in THE_SUMS do

What you've shown is not a bug. If M is a module, then using the statement for x in M do implies that has a ModuleIterator or has some form of indexing implemented. Thus, the thing after the in needs to be a list, set, or other indexable structure. If THE_SUMS is a 1-element list of modules, then op(THE_SUMS) is just a module, not a sequence of modules.

The problem has nothing to do with scoping, name spaces, or whether the code is in a worksheet or library. Your attempt at making a MWE worked because you used instead of op(L).

Like this:

solve(x^(1/x)=y, x);
subsindets(%, specfunc(LambertW), L-> LambertW(k, op(L))); 
Sol:= unapply(%, [k,y]):
Sol~([-1, 0], 1.2);

 [14.76745838, 1.257734541]

The two functions are simple enough that Maple can solve your problems for arbitrary coefficents (this means using convert(..., FormalPowerSeries) rather than commands series or taylor). Note that sin(x)*cos(x) = sin(2*x)/2, by standard trig identities. This means that the ratio of the coefficients of the degree-d terms will be (2^d)/2. We can get Maple to verify that directly:

f:= [sin(x)*cos(x), sin(x)];
S:= convert~(f, FormalPowerSeries);

#Taylor polynomials: Degree 9 corresponds to k=4:
value(eval(S, infinity= 4));

#Ratio of coefficients: x^d corresponds to k = (d-1)/2:
simplify(`/`(eval(op~(1, S), map2(op, [2,1], S)=~ (d-1)/2)[]));


The problem with using unevaluation quotes is that you still need to know the name to put in those quotes. And if you know the name, you might as well put it in string quotes in the first place. So, I don't see much practical value in unevaluation quotes for this.

On the other hand, suppose that you want to list, as strings, all the locals in the current procedure, regardless of whether they have been assigned values. In that case, you can do this:

P:= proc() 
local a:= 2, b:= 7, x;
    convert~([op](2, thisproc), string)
end proc:
                        ["a", "b", "x"]


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